Effects of inertial and kinematic interaction on seismic behavior of pile with embedded foundation

Soil Dynamics and Earthquake Engineering 25 (2005) 753–762 www.elsevier.com/locate/soildyn

Effects of inertial and kinematic interaction on seismic behavior of pile with embedded foundation Kohji Tokimatsua,*, Hiroko Suzukia, Masayoshi Satob a

Department of Architecture and Building Engineering, Tokyo Institute of Technology 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan b Hyogo Earthquake Engineering Research Center, National Research Institute for Earth Science and Disaster Prevention, Nishikameya 1501-21, Shijimi, MIki-shi, Hyogo-ken 673-0515, Japan Accepted 11 November 2004

Abstract Effects of inertial and kinematic forces on pile stresses are studied based on large shaking table tests on pile-structure models with a foundation embedded in dry and liquefiable sand deposits. The test results show that, if the natural period of the superstructure, Tb, is less than that of the ground, Tg, the ground displacement tends to be in phase with the inertial force from the superstructure, increasing the shear force transmitted to the pile. In contrast, if Tb is greater than Tg, the ground displacement tends to be out of phase with the inertial force, restraining the pile stress from increasing. With the effects of earth pressures on the embedded foundation and pile incorporated in, pseudo-static analysis is conducted to estimate maximum moment distribution in pile. It is assumed that the maximum moment is equal to the sum of the two stresses caused by the inertial and kinematic effects if Tb!Tg or the square root of the sum of the squares of the two if TbOTg. The estimated pile stresses are in good agreement with the observed ones regardless of the occurrence of soil liquefaction. q 2005 Elsevier Ltd. All rights reserved. Keywords: Large shaking table test; Pile; Dynamic interaction; Liquefaction; Pseudo-static analysis

1. Introduction The Hyogoken-Nambu earthquake (MZ7.2) that occurred on January 17, 1995, induced not only structural damage but also geotechnical problem in many buildings in the affected area. In particular, many buildings supported on piles in the liquefied and laterally spreading area settled and/or tilted without significant damage to their superstructures. Similar foundation distress was also observed at quite a few buildings in the non-liquefied area. Field investigation and subsequent analyses after the earthquake confirmed that kinematic effects arising from the ground movement as well as inertial effects from superstructure had significant impact on the damage to pile foundations [1], as schematically shown in Fig. 1. While the inertial force from the superstructure dominates in stiff and/or non-liquefied

* Corresponding author. Tel.: C81 3 5734 3160; fax: C81 3 5734 2925. E-mail addresses: [email protected] (K. Tokimatsu), hsuzuki@ arch.titech.ac.jp (H. Suzuki).

0267-7261/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2004.11.018

ground (Case I), not only the inertial force but also the kinematic force comes to play an important role in soft and/ or liquefied grounds (Case II) as well as in laterally spreading ground (Case III). This suggests that both effects are properly taken into account in seismic design of pile foundations. These effects have therefore been studied based on physical model tests with centrifuge shakers or large shaking tables and numerical analyses (e.g. Boulanger et al. [2], Dobry et al. [3], Mitsuji et al. [4], Nishimura et al. [5,6]). Little is known, however, concerning the degree of contribution of the two effects. The objective of this paper is to examine the effects of inertial and kinematic forces on pile stresses based on the results of large shaking table tests on pile-structure models with a foundation embedded in dry and saturated sand deposits and to discuss how these two effects are taken into account in the pseudo-static analysis such as Beam-onWinkler-springs method. The kinematic force includes not only the horizontal subgrade reaction acting on pile (p–y behavior) but also the earth pressure acting on the embedded part of the foundation. Since the latter could have dominant effect over the former when the foundation is embedded, the discussions on kinematic effect in this paper restrict to

754

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

Inertial Force

I) During shaking without liquefaction

Bending Moment

Inertial Force

II) During shaking after liquefaction

Ground Displacement

III-a) Residual ground displacement after earthquake

III-b) Lateral ground displacement after earthquake

Fig. 1. Effects of inertial and kinematic forces on piles.

the earth pressure acting on the embedded foundation. The p–y behavior observed in the same shaking table test has already been described elsewhere [7].

2. Large shaking table tests To investigate the effects of inertial and kinematic forces qualitatively, several series of shaking table tests were conducted on soil-pile-structure systems using the shaking table facility at the National Research Institute for Earth Science and Disaster Prevention (NIED) [7–10]. Fig. 2 summarizes the test series in which a pile-structure system was constructed in either dry or liquefiable saturated sand in a large laminated shear box. The dimensions of the shear box were 4.6 or 6.1 m in height, 12.0 m in width and 3.5 m in length. Model series IDs starting with the letters D and S indicate those tested with dry and saturated liquefiable sands, respectively. The soil used for dry sand deposit was Nikko Sand (emaxZ0.98, eminZ0.65 and D50Z0.42 mm). The relative densities were about 80% for the tests. The soil profile in the liquefaction tests consisted of three layers including a top dry sand layer 0.5 m thick, a liquefiable sand layer 4 m thick and an underlying dense gravelly layer about

1.5 m thick. The sand used was Kasumigaura Sand (emaxZ 0.961, eminZ0.570, D50Z0.31 mm and FcZ5.4%). A cone penetration test was made before each shaking table test to characterize the density profile of the deposit with depth. A 2!2 steel pile group that supported a foundation with or without a superstructure was used. Each pile had a diameter of 165.2 mm with a 3.7 mm wall thickness, and their tips were connected to the container base with pin joints and their heads were fixed to the foundation that was embedded in the ground to a depth of 50 cm. Series ID containing 1 at the end had a foundation of a weight 16.7 kN, while IDs containing L and S at the end had a foundation of 20.6 kN with a superstructure of 139.3 kN. The natural period of the superstructure for series ID containing S at the end was 0.06 or 0.2 s, which is shorter than that of the non-liquefied ground, whereas that containing L was 0.7 or 0.8 s, which is longer than that of the nonliquefied ground but shorter than that of the liquefied ground. The soil-pile-structure system was heavily instrumented with accelerometers, displacement transducers, strain gauges, and, if saturated, pore water pressure transducers, as shown in Fig. 3. In particular, the accelerometers of piles and the ground were measured at every 500 mm with depth and the bending strains of all piles at every 100–250 mm.

Fig. 2. Soil-pile-structure model series in shaking table tests.

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

Moment (kNm)

Acceleration (m/s2)

5

755

DB1

0 (a) Foundation

-5 5

DB1

0 -5 12

(b) Ground surface

DB1

0 (c) Pile head

-12 5

DBS

In these tests, an artificial ground motion called Rinkai, produced as an earthquake in Southern Kanto district in Japan, was used as an input base acceleration to the shaking table. The test results estimated in this paper are those having a peak acceleration of 2.4 m/s2. Prior to each of the main tests, a shaking table test was conducted with a maximum acceleration of 0.2–0.3 m/s2, to estimate the natural period of the ground at a small strain level. The results showed that they were about 0.16 s for a dry sand deposit and 0.3 s for a non-liquefied saturated sand deposit.

-5 5

(d) Superstructure

DBS

0 -5 5

(e) Foundation

DBS

0 (f) Ground surface

-5 Moment (kNm)

Fig. 3. Soil-pile-structure model layout.

Acceleration (m/s2)

0

12 DBS 0 (g) Pile head

-12 5

DBL

Fig. 4 shows time histories of acceleration of ground surface, foundation and superstructure, and bending moment at the pile head in series DB1, DBS and DBL, together with the input base acceleration. The bending moment was computed from the observed bending strain. Although the accelerations of the ground, foundation and superstructure of the three tests are almost equal with each other, their bending moments are quite different. Namely, the bending moment in series DBS with a superstructure is almost twice that in series DB1 without a superstructure, indicating that the inertial force from the superstructure plays an important role. The bending moment in series DBL with a superstructure, in contrast, is significantly smaller than that in series DBS, being almost equal to that in series DB1 without a superstructure. This suggests that not only the inertial force from the superstructure but also other factors such as the ground displacement have a significant influence on the bending moment. To investigate factors affecting stress in piles, the forces acting on the foundation are modeled as shown in Fig. 5. Neglecting the friction between foundation and soil, the total earth pressure acting on the foundation is defined as [9]: PE Z PEp K PEa Z Q K F

(h) Superstructure

-5 5

DBL

0 -5

(i) Foundation

5

DBL

0

Acceleration Moment (m/s2) (kNm)

3. Effect of ground displacement and inertial force on pile stress in dry sand

Acceleration (m/s2)

0

(j) Ground surface

-5 12 DBL 0

(k) Pile head

-12 5 RINKAI 0

(l) Input motion

-5

0

10

20 30 Time (s)

50

Fig. 4. Time histories of observed values in non-liquefied shaking table tests.

(1)

in which PE is the total earth pressure, PEp and PEa are the earth pressures on the passive and active sides, Q is the shear

40

Fig. 5. Force acting on foundation.

756

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

F

F

PE

PE

Q

Q

(a) DBS

(b) DBL

Fig. 7. Total earth pressure acting on foundation in series DBS and DBL.

the pile (Figs. 6(f) and 7(b)). It is interesting to note that the inertial force is in phase in series DBS (Fig. 6(g)) and out of phase in series DBL (Fig. 6(h)) with the ground displacement. To examine the combined effects of kinematic and inertial forces, Figs. 8(a)–(c) and 9(a)–(c) show the distributions of bending moment in pile when either bending moment, soil displacement or inertial force takes its peak value, together with the displacements of pile and soil for the three bending moment distributions in plates (d)–(f) of the same figure. The length of the arrow in the figure indicates the magnitudes of the inertial force and total earth pressure. In series DBS shown in Fig. 8, the distributions of bending moment and displacement of the pile and soil in the three cases are almost the same, as the maximum bending moment occurs when both the inertial force and soil displacement take their maxima. The moment distribution

0

Depth (m)

force at the pile heads computed from the differentiation of observed bending moment, and F is the total inertial force from the superstructure and foundation. Fig. 6 compares the relations of the inertial force with the bending moment, shear force, total earth pressure and ground surface displacement in series DBS and DBL. The shear force is almost equivalent to the inertial force in series DBS in Fig. 6(c), while the former is significantly smaller than the later in series DBL in Fig. 6(d). This indicates that most of the inertial force is transmitted to the shear force in pile in series DBS, contributing to the large bending moment; however, this is not the case in series DBL. The difference in transmitted shear stress between the two tests is probably caused by the different actions of earth pressure against the inertial force, as shown in Fig. 7. The earth pressure in series DBS is out of phase with the inertial force and does not contribute toward reducing the shear force transmitted to the pile (Figs. 6(e) and 7(a)). In series DBL, in contrast, the earth pressure is in phase with and acts against the inertial force, reducing the shear force transmitted to

1

2

3 Moment Max.

(a) 4

-5

0

5

(b)

Ground disp. Max

10 15 -5 0

5

(c)

10 15 -5 0

Inertial force Max.

5

10 15

Bending Moment (kNm) 0

F=71 kN

F=55 kN PE=0 kN

F=78 kN PE=12k N

PE=0 kN

1

Depth (m)

Fig. 6. Relations of inertial force with bending moment, shear force, total earth pressure, and ground displacement in series DBS and DBL.

DBS

2

Pile Ground

3

4

(d) 0

Moment Max.

10

(e)

20

0

Ground disp. Max

10

Inertial force Max.

(f)

20

0

10

20

Displacement (mm) Fig. 8. Distributions of bending moment and displacement in series DBS.

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

0

DBL

Depth (m)

1

2

3

4

Inertial force Max.

Ground disp. Max (c) (a) Moment Max. (b)

-5

0

5

10 15 -5

0

5

10 15 -5

0

5

10 15

Bending Moment (kNm) 0

PE=8 kN

PE=2 kN

PE=24k N

4. Effects of ground displacement and inertial force on pile stress during liquefaction

Depth (m)

1

2

Pile Ground

3

4

Inertial force Max.

Ground disp. (d) Moment Max. (e) Max (f)

0

10

20

0

10

20

0

10

20

Displacement (mm) Fig. 9. Distributions of bending moment and displacement in series DBL.

Fourier S pectrum (m/s)

shown in Fig. 8(a) is, therefore, considered to be due to the combined effects of inertial force and ground displacement. In series DBL shown in Fig. 9, the distributions of bending moment and displacement of the pile and soil in the three cases are different from each other. In Fig. 9(e), the soil displacement takes the maximum with a small inertial force, producing the bending moment distribution due mainly to the kinematic effect. In Fig. 9(f), the inertial force dominates with negligible soil displacement, producing the bending moment distribution solely due to the inertial effect. The maximum bending moment at the pile head occurs in Fig. 9(d) when the inertial force and ground displacement do not take their maxima. Fig. 10 shows Fourier spectra of the input motion and the recorded accelerations of the ground surface,

6

(a)

4

Superstructure Foundation Ground surface Input motion

(b)

2 0

DBS 0.1

1

foundation and superstructure. Note that the Fourier spectrum of the foundation in series DBL is overlapped with that of the ground surface. In series DBS, the Fourier spectrum of the superstructure has a peak at the same period as that of the ground surface and foundation. In series DBL, the Fourier spectrum of the superstructure has a peak at a period greater than that of the ground surface and foundation. It is conceivable, therefore, that the effects of soil displacement and inertial force tend to be in phase if the natural period of superstructure is shorter than that of the ground but that they are out of phase if the natural period of superstructure is longer than that of the ground.

F=60 kN

F=38 kN

F=50 kN

757

0.1 Period(s)

DBL 1

Fig. 10. Fourier spectra of acceleration in series DBS and DBL.

To investigate whether the findings in dry sand are valid in liquefiable saturated sand, a similar examination was made for the other series conducted with saturated sand. Fig. 11 shows time histories of the accelerations of superstructure and foundation, soil displacement, bending moment at the pile head and pore water pressure ratio, for series SB1, SBS, and SBL. Soil liquefaction develops throughout the saturated sand layer in 20 s, accompanied by an increase in ground surface displacement. The observed accelerations of foundation and superstructure are significantly smaller than those in dry sand shown in Fig. 4. The bending moment after liquefaction becomes considerably larger than not only that before liquefaction but also that in any of the tests with dry sand shown in Fig. 4. Considering the difference in acceleration and ground displacement before and after liquefaction and between dry and saturated sand, the combined effects of inertial and kinematic forces on pile stresses might have changed in the course of soil liquefaction. Figs. 12 and 13 compare the relations of the inertial force with the bending moment, shear force, total earth pressure and ground displacement, for three time segments (0–10, 10–20, and 20–50 s) in series SBS and SBL. The bending moments after liquefaction in both cases are larger than those before liquefaction (Figs. 12 and 13(a)– (c)). This is probably caused by the increase in shear force arising from kinematic effects, as shown in Figs. 12(d)–(f) and 13(d)–(f). Namely, the shear force, which is less than the inertial force before liquefaction, becomes equal to or greater than the inertial force after liquefaction. The drastic change in shear force transfer to the pile with the development of liquefaction is induced by the change in action of earth pressure against the inertial force, as shown in Figs. 12(g)–(i) and 13(g)–(i). The total earth pressure that acts against the inertial force before liquefaction begins to act with the inertial force, increasing the shear force to the pile after liquefaction, as schematically shown in Fig. 14.

758

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

Fig. 12. Relations of inertial force with bending moment, shear force, total earth pressure and ground displacement in series SBS.

Fig. 11. Time histories of observed values in liquefaction shaking table tests in series SB1, SBS and SBL.

The circle in plates of Figs. 12(j)–(l) and 13(j)–(l) corresponds to the time at which the bending moment at the pile head is the largest within a time segment of 0.5 s. After liquefaction (20–50 s), the maximum bending moment occurs when both soil displacement and inertial force get large. This is because the natural period of the liquefied soil is always greater than that of the superstructure in both series SBS and SBL and thus the effects of soil displacement and inertial force are in phase with each other, increasing the bending moment in piles. The trend is consistent with that observed in dry sand.

Fig. 13. Relations of inertial force with bending moment, shear force, total earth pressure and ground displacement in series SBL.

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

F

759

F

PE

PE

Q

Q

(a) Before liquefaction

(b) During liquefaction

Fig. 14. Change in action of earth pressure.

5. Pseudo-static analysis Seismic design of pile foundations may be made based on either dynamic response analysis or pseudo-static analysis. In this study, a pseudo-static analysis based on Beam-on-Winkler-springs method is conducted to examine its effectiveness in estimating pile stresses in the large shaking table tests. Simplified pseudo-static design methods using p–y curves for pile foundations in which the effects of ground displacement (Case I in Fig. 1) can be neglected are based on the following equation [11,12]: EI

d4 y Z Kkh Bp y dz4

(2)

in which E and I are the Young’s modulus and the moment of inertia of pile, y is the horizontal displacement of a pile, z is the depth, kh is the coefficient of horizontal subgrade reaction, and B is the pile diameter. If the ground movement cannot be neglected during and after an earthquake (Cases II and III in Fig. 1), the equation may be given by [13,14]: EI

d4 y Z Kkh Bp ðy K yg Þ dz4

Fig. 15. Combination of inertial and kinematic effects on pile stresses in Case II.

5.2. Earth pressure acting on embedded foundation The total earth pressure PE defined in Fig. 5, which controls the stress transfer between soil and foundation in Eq. (3), can be given by [9,10]: 1 PE Z PEp K PEa Z gH 2 BðKEp K KEa Þ 2

in which g is a unit weight of soil, H and B are the height and width of foundation and KEa and KEp are the coefficients of earth pressures on the active and passive sides. To take into account the effect of relative displacement between soil and foundation on the earth pressure, Zhang et al. [15] introduced the earth pressure coefficients, KEa and KEp, which can be expressed by the following equations as a function of lateral strain parameter, R:

(3) KEa Z

in which yg is the ground displacement. 5.1. Combination of inertial and kinematic forces The pile stresses in Cases I and III shown in Fig. 1 can be estimated using either Eq. (2) with the effects of inertial force or Eq. (3) with the effects of ground displacement; however, this is not the case in Case II where both inertial force and ground displacement dominate. Based on the discussion on Figs. 7–9 and 14, when the natural period of the superstructure is smaller than that of the ground, the pile stress may be estimated, provided that both inertial and kinematic forces are in phase and act on the pile at the same time (Method 1 in Fig. 15(a)). When the natural period of the superstructure is longer than that of the ground, the pile stress may be given by the square root of the sum of the squares of the two values estimated, provided that the inertial and kinematic forces are out of phase with each other and act on the pile separately (Method 2 in Fig. 15(b)).

(4)

2 cos2 ðf K iÞ i cosðdmob C iÞð1 K RÞIE:1 (5)

cos2 ðf K iÞð1 C RÞ C cos


 1 cos2 ðf K iÞ K1 KEp Z 1 C ðR K 1Þ 2 cos i cosðdmob C iÞIE:2 IE:1 IE:2

!

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# sinðf C dmob Þsinðf K iÞ Z 1G cosðdmob C iÞ

(6)

"

(8)

tan i Z ki $



jDr j R Z max K1 Da $

(7)



jDr j R Z min 3; 3 Dp

0:5 % ðActive SideÞ

(9)

ðPassive SideÞ

(10)

0:5 %

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

Earth Pressure Coefficient KEa or K Ep

760

5

always equal to the difference between the two as defined by Eq. (4). The effectiveness of the abovementioned seismic earth pressure model has been described elsewhere [10].

Lateral Strain Parameter, R -1 0 1 2 3

4 3

5.3. p–y relation

2

The relation of the subgrade reaction, p, acting on a unit length of the pile, with the relative displacement between pile and soil, yr (ZyKyg), often called p–y relation, which also controls the stress transfer between soil and pile in Eq. (3), is given by:

Active state Passive state

KEp

1 0

∆a

0 ∆p Relative Displacement, ∆r

KEa

Fig. 16. Earth pressure coefficient with relative displacement and lateral strain parameter.

1 dmob Z ð1 K RÞda 2

ðActive SideÞ

(11)

ðPassive SideÞ

(12)

in which f is the internal friction angle of sand, i is the angle of seismic coefficient in the horizontal direction (ki), R is the assigned value from K1 to 0 in the active side and from 0 to 3 in the passive side, Dr is the relative displacement between soil and foundation, d is the friction angle of the surface of the foundation, da and dp are friction angles of sand at the active and passive states, and Da and Dp are reference relative displacements at active and passive states, expressed as: Da Z bH

(13)

Dp Z bH

(14)

in which a is equal to 0.001–0.005, and b is equal to 0.05–0.1. Fig. 16 shows the coefficient of earth pressure with the lateral strain parameter and the relative displacement between soil and foundation. Thus, by introducing R as a function of relative displacement given by Eqs. (9) and (10), the coefficient of earth pressure in any stress state between the active and passive states can be determined. Depending on the relative displacement between soil and foundation, the passive-side earth pressure acts on one side of the foundation with the active-side earth pressure on the opposite side of the foundation, as shown in Fig. 17. Thus, the total earth pressure acting on the foundation is F

(15)

in which kh is the coefficient of subgrade reaction given by [2]: kh Z kh1

1 dmob Z ðR K 1Þdp 2

P Ea

p Z k h Bp y r

2b 1 C jyr =y1 j

(16)

in which b is the scaling factor for liquefied soil, y1 is the reference value of yr, and kh1 is the reference value of kh defined as [6]: kh1 Z 80E0 BK0:75 0

(17)

E0 Z 0:7 N

(18) 2

in which E0 (MN/m ) is the Young’s modulus of soil, N is the SPT N-value, and B0 is the pile diameter in cm. The effectiveness of the abovementioned p–y model has been described elsewhere [7].

6. Estimation of pile stresses in shaking table tests based on psuedo-static analysis To demonstrate the effectiveness of the pseudo-static analysis method combined with the kinematic effects described in the previous section, the bending moment and displacement distributions of four shaking table tests with dry and saturated sands (series DBS, DBL, SBS, and SBL) are computed. Fig. 18 shows the soil-pile-structure model used in the analysis, in which the inertial force and ground displacement are simultaneously or separately

F

P Ep

P Ep

P Ea

y g : Ground displacement y f : Foundation displacement

(a) yg < y f

(b) yg > y f

Fig. 17. Active and passive earth pressures acting on foundation.

Fig. 18. Soil-pile-structure model used in analysis.

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

761

0

0

(a)

(b)

(c)

(d)

1

Fmax=78kN ygmax=10mm

2

3

Depth (m)

Depth (m)

1

Fmax=60kN ygmax=9mm

DBS 0

3

5

DBL

5 10 15 -5 0 5 Bending Moment (kNm)

10

15

Fmax=28kN ygmax=68mm

Fmax=24kN ygmax=75mm

4

Estimated Observed

4 -5

2

SBS

-20 -10

SBL

0 10 20 -20 -10 0 Bending Moment (kNm)

10

20

Fig. 19. Distributions of observed and estimated bending moment in shaking table tests.

0

(a)

0

(b)

(c)

(d)

1

Depth (m)

Depth (m)

1

2

3

0

5

10

15 -5

3 4

Estimated Observed

DBS 4 -5

2

0

5

DBL

5

10

-20 0

Displacement (mm)

15

SBS 20 40 60 80 -20 0

SBL 20 40 60 80

Displacement (mm)

Fig. 20. Distributions of observed and estimated pile displacement in shaking table tests.

considered, depending on the natural period of the superstructure relative to that of the ground (see Fig. 15). Namely, the pile stresses in series DBS, SBS, and SBL are estimated by method 1 as the natural period of the superstructure is shorter than that of the ground and those in series DBL is estimated by method 2, as the natural period of the superstructure is greater than that of the superstructure. It is assumed that, with the inertial force equal to the observed maximum, Fmax, the ground displacement above the base of the foundation is equal to the observed maximum, ygmax, at the ground surface and decreases linearly to zero at the base of the container for dry sand or at the bottom of the liquefied layer for saturated sand. Note that the soil displacement assumed in Fig. 18 is that for the simulation of large shaking table test results only. The soil displacement for seismic design of pile foundations in the field should be made based on either numerical approach such as SHAKE [16] or empirical approach such as that proposed by Tokimatsu and Asaka [17]. The N-values to be used in Eq. (17) for p–y relation were estimated from the CPT-values measured prior to the shaking table test [18]. It is also assumed that b is 0.1 for the liquefied sand and 1.0 for the non-liquefied sand and gravel,

y1 in Eq. (16) is 1.0% of pile diameter [12], f is 30 degrees, da and dp are 15 degrees, and that Da and Dp are 0.5 and 5% for the height of the foundation [10]. Figs. 19 and 20 compare the observed and computed bending moment and displacement distributions of the pile in four tests, together with the corresponding observed maximum inertial force and ground displacement, Fmax and ygmax. The observed values are shown at which the maximum bending moment at the pile head occurs. The computed distributions of the bending moment and displacement agree reasonably well with the observed values, indicating that the pseudo-static analysis together with the consideration of the effects of ground displacement is promising for estimating pile stress as well as deformation.

7. Conclusions The effects of inertial and kinematic forces on pile stresses have been studied based on large shaking table tests on pile-structure models with foundation embedment in dry and liquefiable saturated sand deposits. A pseudo-static

762

K. Tokimatsu et al. / Soil Dynamics and Earthquake Engineering 25 (2005) 753–762

analysis, in which the effects of earth pressures on the embedded foundation as well as on pile are incorporated, has been proposed and used for estimating pile stress and displacement in the tests. The results and analysis have shown the following: (1) If the natural period of the superstructure is less than that of the ground, the kinematic force tends to be in phase with the inertial force, increasing the stress in piles. The maximum pile stress occurs when both inertial force and ground displacement take the peaks and act in the same direction. (2) If the natural period of the superstructure is greater than that of the ground, the kinematic force tends to be out of phase with the inertial force, restraining the pile stress from increasing. The maximum pile stress tends to occur when both inertial force and ground displacement do not become maxima at the same time. (3) The estimated bending moment and deformation of the pile from the pseudo-static analysis are in good agreement with the observed values both in dry and liquefied saturated sands. This suggests that the pseudostatic analysis is promising for estimating pile stress and deformation mode with a reasonable degree of accuracy.

Acknowledgements The study described herein was made possible through two research projects related to soil-pile-structure interaction using the large shaking table at the NIED, including Special Project for Earthquake Disaster Mitigation in Urban Areas, supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT). The authors express their sincere thanks to the above organization.

References [1] BTL Committee, Research report on liquefaction and lateral spreading in the Hyogoken-Nambu earthquake; 1998 (in Japanese). [2] Boulanger RW, Curras JC, Kuter BL, Wilson DW, Abghari A. Seismic soil-pile-structure interaction experiments and analyses. J Geotech Geoenviron Eng ASCE 1999;125(9):750–9.

[3] Dobry R, Abdoun T, O’Rourke TD, Goh SH. Single piles in lateral spreads: Field bending moment evaluation. J Geotech Geoenviron Eng ASCE 2003;129(10):879–89. [4] Mitsuji K, Yokoi Y, Sugimoto Y. Evaluation of horizontal load of piles based on results of dynamic analysis (Part 2 proposal of horizontal load). Proceedings of twenty-eighth Japan national conference on geotechnical engineering. vol. 2 1993 pp 1847–1848 (in Japanese). [5] Nishimura A, Murono Y, Nagatsuma S. Experimental studies on the seismic design method for pile foundations in the soft ground (Part 1)– (Part 3). Proceedings of thirty-second Japan national conference on geotechnical engineering. vol. 1 1997 pp 961–966 (in Japanese). [6] Nishimura A, Murono Y, Nagatsuma S. Seismic response characteristics of pile foundation in soft ground and its application to seismic design. Proceedings of thirty-third Japan national conference on geotechnical engineering. vol.1 1998 pp 1079–1080 (in Japanese). [7] Tokimatsu K, Suzuki H, Saeki S. Modeling of horizontal subgrade reaction of pile during liquefaction based on large shaking table. J Struct Construct Eng AIJ 2002;559:135–41 (in Japanese). [8] Tamura S, Tsuchiya T, Suzuki Y, Fujii S, Saeki E, Tokimatsu K. Shaking table tests of pile foundation on liquefied soil using largescale laminar box (Part 1 outline of test). Proceedings of thirty-fifth Japan national conference on geotechnical engineering. vol. 2 2000 pp 1907–1908 (in Japanese). [9] Tamura S, Miyazaki M, Fujii S, Tsuchiya T, Tokimatsu K. Earth pressure acting on embedded footing during soil liquefaction by largescale shaking table test. Proceedings of forth international conference on recent advances in geotechnical earthquake engineering and soil dynamics, 2001, Paper No. 6.19. [10] Tokimatsu K, Tamura S, Miyazaki M, Yoshizawa M. Evaluation of seismic earth pressure acting on embedded footing based on liquefaction test using large scale shear box. J Struct Construct Eng AIJ 2003;570:101–6 (in Japanese). [11] Architectural Institute of Japan, Recommendations for design of building foundations; 1988, 2001 (in Japanese). [12] Japan Road Association, Specifications for road bridges, vol. IV. 1997 (in Japanese). [13] Nishimura A. Design of structures considering ground displacement. Kisoko 1978;6(7):48–56 (in Japanese). [14] Tokimatsu K, Nomura S. Effects of ground deformation on pile stresses during soil liquefaction. J Struct Construct Eng AIJ 1991;426: 107–12 (in Japanese). [15] Zhang J-M, Shamoto Y, Tokimatsu K. Evaluation of earth pressure under any lateral displacement. Soils Found JGS 1998;38(2):143–63. [16] Schnabel PB, Lysmer J, Seed HB. Shake-A computer program for earthquake response analysis of horizontally layered sites, Report No. EERC72-12, University of California, Berkeley; 1972. [17] Tokimatsu K, Asaka Y. Effects of liquefaction-induced ground displacements on pile performance in the 1995 Hyogoken-Nambu earthquake. Soils Found JGS 1998;(Special issue):163–77. [18] Yamada K, Kamao S, Yoshino H, Masuda Y. Correlation between Nvalue and cone index. Tsuchi-to-Kiso JGS 1992;40(8):5–10 (in Japanese).